Comment on УStrong signature of the active Sun in 100 years of terrestrial insolation
dataФ by W. Weber

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Ann. Phys. (Berlin) 523, No. 11, 946 – 950 (2011) / DOI 10.1002/andp.201100179
Comment on “Strong signature of the active Sun in 100 years
of terrestrial insolation data” by W. Weber
Georg Feulner∗
Earth System Analysis, Potsdam Institute for Climate Impact Research (PIK), P.O. Box 60 12 03,
14412 Potsdam, Germany
Received 28 July 2011, accepted 10 August 2011 by U. Eckern
Published online 20 September 2011
Key words Climate, solar activity, solar irradiance, cosmic rays.
An analysis of ground-based observations of solar irradiance was recently published in this journal, reporting an apparent increase of solar irradiance on the ground of the order of 1% between solar minima and
maxima [1]. Since the corresponding variations in total solar irradiance on top of the atmosphere are accurately determined from satellite observations to be of the order of 0.1% only [2], the one order of magnitude
stronger effect in the terrestrial insolation data was interpreted as evidence for cosmic-ray induced aerosol
formation in the atmosphere. In my opinion, however, this result does not reflect reality. Using the energy
budget of Earth’s surface, I show that changes of ground-based insolation with the solar cycle of the order
of 1% between solar minima and maxima would result in large surface air temperature variations which are
inconsistent with the instrumental record. It would appear that the strong variations of terrestrial irradiance
found by [1] are due to the uncorrected effects of volcanic or local aerosols and seasonal variations. Taking
these effects into account, I find a variation of terrestrial insolation with solar activity which is of the same
order as the one measured from space, bringing the surface energy budget into agreement with the solar
signal detected in temperature data.
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Earth’s surface energy budget
Using a simple argument based on the energy budget at Earth’s surface one can show that a variation of
terrestrial insolation with solar activity on the percentage level – as reported in [1] – would lead to unrealistically large temperature fluctuations which are not observed in the instrumental surface temperature
record. To first order, the relationship between surface temperature Ts and terrestrial insolation Is is governed by the balance between the absorbed short-wave radiation Is (1 − αs ) and the long-wave emission
εσTs4 according to the Stefan-Boltzmann law, with the surface reflectivity or albedo αs , the emissivity
ε and the Stefan-Boltzmann constant σ. Therefore, changes in temperature dT are related to changes in
insolation dI by
dT
1 dI
,
Ts
4 Is
(1)
since changes of surface albedo can be neglected for such small irradiance variations. Conventional wisdom
suggests that terrestrial insolation Is varies with the solar cycle in the same way as the total solar irradiance
(TSI) above the atmosphere, i.e. dI/Is 0.1% [2]. Using this value and an average surface temperature
of Ts = 288 K yields an expected temperature variation over the solar cycle of dT 0.07 K. This simple
approximation ignores feedbacks in the climate system (due to clouds, water vapour, ice and changes in
the lapse rate). The combination of these effects is generally considered to act as a positive feedback, the
estimate above can thus be considered a lower limit.
∗
E-mail: feulner@pik-potsdam.de
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Ann. Phys. (Berlin) 523, No. 11 (2011)
947
A more appropriate estimate for the temperature response dT to changes in solar irradiance dI including
these feedbacks is given by the relation
dT = λt dF,
(2)
Temp. Anomaly (K)
Temp. Anomaly (K)
with the change in radiative forcing dF = (1 − α)dI/4 (the change dI in incoming solar radiation I 1361 W m−2 corrected for Earth’s albedo α 0.3 and geometry) and the transient climate sensitivity
λt 0.4 K/(W m−2 ) [3] describing the short-term response of the climate system to changes. For a change
of 0.1% in insolation this yields dT 0.1 K, in excellent agreement with the value derived from global
surface air temperature data [4, 5].
This estimate is interesting for two reasons: First, it shows that most of the observed solar-cycle global
temperature variation can be explained by changes in top-of-the-atmosphere irradiance alone. The remainder is likely due to well documented effects of changes in ultraviolet radiation, leaving little room for more
speculative effects of cosmic rays. Secondly, a terrestrial insolation variation with solar activity one magnitude larger than the TSI changes (as suggested by the results in [1]) would lead to global temperature
changes of dT 1 K between solar maxima and minima (Fig. 1b), a result clearly in conflict with the
instrumental surface air temperature record (e.g. [6]) which does not exhibit such large variations over the
11-year solar cycle (see Fig. 1a).
1.5
(a)
1.0
0.5
0.0
−0.5
1.5
(b)
1.0
0.5
0.0
−0.5
1880
1900
1920
1940
1960
1980
2000
Year
Fig. 1 (a) Monthly values for the global surface air temperature anomaly (relative to the average 1951–
1980) [7]. Other global surface temperature datasets look very similar. (b) Monthly temperature anomalies
due to the 11-year solar cycle according to [4] (black line) on the same scale as panel (a). The grey line
indicates the response expected for a ten-times larger variation in terrestrial irradiance as suggested by [1]
which is inconsistent with the temperature record shown in panel (a).
This discrepancy between the strong variation of terrestrial insolation reported in [1] and the energy
budget at Earth’s surface suggests that the data analysis in [1] is biased by systematic effects not related to
solar activity changes, a hypothesis which will be explored in the next section.
2 Analysis of the terrestrial insolation data
The analysis of ground-based insolation data in [1] neglects the effects of atmospheric aerosols from volcanoes or local pollution and seasonal variations, which in my opinion feigns a stronger influence of solar
activity on terrestrial insolation. These arguments will be briefly summarised in this section, the complete
re-analysis of the data is discussed in detail in [8].
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G. Feulner: Comment
The bias resulting from volcanic aerosols and pollution is illustrated in Fig. 2. During the time period
1924–1955 covered by the Smithsonian Astrophysical Observatory (SAO) data [9] analysed in [1], the
years 1928–1934 and 1951–1955 were affected by aerosols from well documented volcanic eruptions and
local pollution [10]. By coincidence, these periods overlap with two out of three of the solar minima during
this interval (Fig. 2a). Since aerosols absorb and scatter incoming light, this results in a lower measured
irradiance on the ground, as can be seen in Fig. 2b. Note that there is no apparent drop in irradiance during
the minimum around 1944 which is unaffected by aerosols, demonstrating that the lower irradiance during
the other two solar minima is indeed driven by aerosols rather than the low solar activity. (Note that the
expected variation of the irradiance with solar activity of the order of 0.1% is too small to be seen with the
naked eye on this scale.)
Fig. 2 (online colour at: www.ann-phys.org) (a) Daily sunspot numbers [11] for the time from 1924 to
1955. (b) Daily values of terrestrial solar irradiance as measured at Cerro Montezuma at airmass 2 during
the same time period. Grey-shading indicates periods affected by volcanic aerosols or local pollution [10].
(c) Scatter function of the irradiance. (d) Reduced irradiance, i.e. the irradiance with the scatter function
subtracted to correct for variations in atmospheric water and aerosol content.
In his reply [12] to this comment, Werner Weber observes that the scatter in the derived TSI during
these periods of active volcanism is not larger than at other times and concludes that the SAO personnel
did not take observations during these time intervals. This is not entirely convincing, however, since the
effects of volcanic aerosols are visible for a few years after the eruptions, and there clearly exist data during
these time periods. I would argue that the small scatter in the TSI demonstrates that the SAO method for
c 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Ann. Phys. (Berlin) 523, No. 11 (2011)
949
correcting the observed irradiance for the measured effects of water vapour and aerosols even work at times
of large volcanic aerosol loads in the atmosphere.
The seasonal bias in the data is a bit more intricate. Terrestrial irradiance exhibits a strong seasonal cycle
(see Fig. 2b). Since days with low and high sunspot numbers are not distributed equally over all seasons
in the SAO data, an analysis of trends of irradiance with sunspot number will be skewed if the seasonal
variations are not corrected [8].
A reanalysis of the data corrected for seasonal variations and without the years affected by volcanic or
other aerosols yields a trend of irradiance with sunspot number which is about a factor of ten smaller than
the one reported in [1], corresponding to a variation of 0.1% between solar maxima and minima as for
the TSI [8]. This variation of terrestrial insolation is in agreement with the temperature changes associated
with the solar cycle [4, 5], see the energy estimate presented in Sect. 1.
Since the publication of the original results in [1], Werner Weber has introduced an improved analysis
technique for the SAO data described in his reply to this comment [12]. Starting with the observation that
the measured terrestrial irradiance shows a second-order dependence on the precipitable water content W
and the brightness A of the solar aureole, a ‘scatter function’ I can be constructed by approximating a
second-order power series in W and A to the observed irradiance (see Fig. 2c for an example). Subtracting
this scatter function I from the irradiance measurements I yields the ‘reduced irradiance’ I which exhibits a drastically reduced scatter as compared to the original irradiance (see Fig. 2d). This method is quite
remarkable and is a legitimate technique to remove the effects of seasons and volcanic aerosols; physically
it is equivalent to correcting the observed terrestrial irradiance for the effects of water vapour and aerosols
in the atmosphere using empirical data.
In addition, however, Werner Weber argues that the scatter function I depends strongly on the sunspot
number R and that the R dependence of I has to be removed by applying a Legendre-type transformation
I → I with Ii = Ii − Ci Ri . The variation of I , however, is more likely caused by the effects of aerosols
rather than by solar activity (see the discussion above and in [8]). Hence by applying the transformation
an unrealistic R dependence of the reduced irradiance I is introduced in [12], leading to an artificially
large variation of the terrestrial irradiance with sunspot number and a striking, yet misleading correlation
between sunspot number and strong variations in the reduced (and transformed) terrestrial irradiance shown
in Fig. 4 in [12].
This effect is best illustrated by the apparent dip in the reduced terrestrial irradiance around the solar
minimum in 1945 in [12]: Looking at the original data, there is no decrease in terrestrial insolation and no
increase in water content or aureole brightness during that time (see Fig. 2 in [12] and Fig. 2c in [8]), yet
Fig. 2 in [12] shows an increase in the transformed scatter function I and a corresponding dip in the reduced
irradiance I = I − I . These features can be naturally explained as artefacts of the transformation based
on the assumption that the scatter function I depends on sunspot number R. Nevertheless, the technique
of scatter reduction (without the transformation) introduced in [12] might offer the possibility to improve
the analysis of terrestrial irradiance trends provided that the effects of solar activity and volcanism can be
reliably separated. Indeed, the trends of the reduced irradiance (un-transformed) with sunspot number are
in agreement with the results found in [8] and thus with the surface energy balance discussed in Sect. 1.
3 Discussion: Solar activity and Earth’s climate
Quantifying the influence of solar activity on Earth’s climate [13] is clearly an important issue, helping to distinguish between natural and anthropogenic causes of climate change. The energy balance of
Earth’s surface (Sect. 1) and investigations of the instrumental temperature record [4, 5] show, however,
that the temperature changes caused by the 11-year solar cycle amount to 0.1 K only, much smaller than
the observed 20th-century warming of about 0.7 K [6]. On longer timescales, extended periods of low
solar activity (‘grand minima’) like the 17th-century Maunder Minimum [14] are associated with a global
cooling of only a few tenths of a degree [15], although regional and seasonal temperature signatures are
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950
G. Feulner: Comment
more pronounced. Furthermore, solar activity appears not to be the dominant cause of the “Little Ice Age”
coinciding with the Maunder Minimum. Both lower greenhouse gas concentrations and strong volcanic
eruptions during the 17th century contributed to the observed cooling [16, 17]. This also means that even
a future grand solar minimum could not offset the much larger temperature rise caused by anthropogenic
greenhouse-gas emissions [18, 19].
Acknowledgements I would like to thank Stefan Rahmstorf for valuable comments and Ulrich Eckern for editorial support. The monthly TSI data were kindly provided by Judith Lean. This research has made use of NASA’s
Astrophysics Data System Bibliographic Services.
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